Abstract: We provide robust estimators for the first canonical correlation and directions of random elements on Hilbert separable spaces by using robust association and scale measures, combined with basis expansions and/or penalizations as a regularization tool. Under regularity conditions, the resulting estimators are consistent. The finite-sample performance of our proposal is illustrated by means of a simulation study that shows that, as expected, the robust method outperforms the existing classical procedure when the data are contaminated. A real data example is also presented.

Keywords words and phrases: Canonical correlation analysis, functional data, robust estimation, smoothing techniques.